John, I have a well-regarded WWII reference which says the 3rd Infantry departed Boston 8 March 1945 and landed at Le Havre, France 18 March 1945. It says further they initially provided a reserve to contain German garrison at St. Nazaire. Were then attached to the 106th Infantry Division from March 16 to June 23. They crossed into Germany April 26 and processed prisoners. They were inactivated at Berlin on 26 November 1946.
Here is a web page with details on the 106th ID (such as dates and locations of command posts, etc) which includes a citation of the attachment of the 3rd Infantry as noted in my reference.